Analysis of Galvanomagnetic de Haas-van Alphen Type Oscillations in Graphite

An analysis has been made of oscillations in the Hall effect and magnetoresistance for graphite single crystals at 4.2°K with the field parallel to the hexagonal axis. Two periods of 2.11×${10}^{-5\mathrm{}}$ ${\mathrm{gauss}}^{-1\mathrm{}}$ and 1.58×${10}^{-5\mathrm{}}$ ${\mathrm{gauss}}^{-1\mathrm{}}$ are shown to be due to the majority electrons and holes, respectively. These same two values were found in both galvanomagnetic effects and are in reasonable agreement with those observed in the susceptibility. There is a phase difference of $\pi$ between the two galvanomagnetic properties. An analysis of the magnetic field dependence of the amplitude incorporating both effects in a "galvanomagnetic ratio," $\frac{\rho }{R}$, has been made giving effective-mass values of $0.030m_0$ for the electrons and $0.060m_0$ for the holes. These are in substantial agreement with those calculated from cyclotron resonance and from the temperature dependence of the susceptibility de Haas-van Alphen oscillations. Corresponding Fermi energies were found to be 0.018 ev for the electrons and 0.012 ev for the holes, giving a very slight band overlap in graphite of 0.030 ev.